| Curve name |
$X_{104}$ |
| Index |
$24$ |
| Level |
$16$ |
| Genus |
$0$ |
| Does the subgroup contain $-I$? |
Yes |
| Generating matrices |
$
\left[ \begin{matrix} 3 & 9 \\ 14 & 7 \end{matrix}\right],
\left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right],
\left[ \begin{matrix} 3 & 3 \\ 2 & 1 \end{matrix}\right],
\left[ \begin{matrix} 1 & 5 \\ 6 & 3 \end{matrix}\right]$ |
| Images in lower levels |
|
| Meaning/Special name |
|
| Chosen covering |
$X_{30}$ |
| Curves that $X_{104}$ minimally covers |
$X_{30}$ |
| Curves that minimally cover $X_{104}$ |
$X_{292}$, $X_{293}$, $X_{294}$, $X_{295}$ |
| Curves that minimally cover $X_{104}$ and have infinitely many rational
points. |
$X_{295}$ |
| Model |
\[\mathbb{P}^{1}, \mathbb{Q}(X_{104}) = \mathbb{Q}(f_{104}), f_{30} =
\frac{-2}{f_{104}^{2}}\] |
| Info about rational points |
None |
| Comments on finding rational points |
None |
| Elliptic curve whose $2$-adic image is the subgroup |
$y^2 + xy = x^3 + x^2 - 58815x - 5514400$, with conductor $4225$ |
| Generic density of odd order reductions |
$13411/43008$ |